Two Pulleys with two acceleration and two tensions (Diagram included)

[Wara]

pulley

Homework Statement

Two masses are attached together by means of light inextensible strings and light frictionless pulleys as shown in the diagram. The system is released and the upper block slides along the table. The coefficient of friction between this block and the table is 0.32. Calculate the magnitude of the tensions (T₁ and T₂) and accelerations while the blocks are acceleration.
http://content.screencast.com/users/Waraa/folders/Snagit/media/bc6a12fc-dd79-4db6-91a4-1057f75aca6e/03.10.2012-15.11.45.png

Homework Equations

(1) m₁a₁ = T₁ - μmg
(2) m₂a_a = m₂g - T₂
(3) 2T₁ = T₂
(4) 2a₂ = a₁

The Attempt at a Solution

T₁ = 113.7N
T₂ = 196N

(1) + (2) + (3) + (4)
m₁a₁ + m₂a_a + 2T₁ + 2a₂ = T₁ - μmg + m₂g - T₂ + T₂ + a₁
2a₂ = T₁ - μmg + m₂g + a₁

I'm stuck right there. Am I even doing it right?

 

[tiny-tim]

Homework Statement

Two masses are attached together by means of light inextensible strings and light frictionless pulleys as shown in the diagram. The system is released and the upper block slides along the table. The coefficient of friction between this block and the table is 0.32. Calculate the magnitude of the tensions (T₁ and T₂) and accelerations while the blocks are acceleration.
http://content.screencast.com/users/Waraa/folders/Snagit/media/bc6a12fc-dd79-4db6-91a4-1057f75aca6e/03.10.2012-15.11.45.png

Homework Equations

(1) m₁a₁ = T₁ - μmg
(2) m₂a_a = m₂g - T₂
(3) 2T₁ = T₂
(4) 2a₂ = a₁

The Attempt at a Solution

T₁ = 113.7N
T₂ = 196N

(1) + (2) + (3) + (4)
m₁a₁ + m₂a_a + 2T₁ + 2a₂ = T₁ - μmg + m₂g - T₂ + T₂ + a₁
2a₂ = T₁ - μmg + m₂g + a₁

I'm stuck right there. Am I even doing it right?

Hi Wara!

(1) m₁a₁ = T₁ - μmg
(2) m₂a_a = m₂g - T₂
(3) 2T₁ = T₂
(4) 2a₂ = a₁

Fine so far!

ok, now you should substitute for a₂ and T₂ from (3) and (4) into (2):

(1) m₁a₁ = T₁ - μmg
(2) m₂a₁/2 = m₂g - 2T₁​

then eliminate T₁

 

[Wara]

Hi Wara!


Fine so far!

ok, now you should substitute for a₂ and T₂ from (3) and (4) into (2):

(1) m₁a₁ = T₁ - μmg
(2) m₂a₁/2 = m₂g - 2T₁​

then eliminate T₁

Thank you so much.